Abstract
Physics textbooks often present items of disciplinary knowledge in a sequential order of topics of the theory under instruction. Such presentation is usually univocal, that is, isolated from alternative claims and contributions regarding the subject matter in the pertinent scientific discourse. We argue that comparing and contrasting the contributions of scientists addressing similar or the same subject could not only enrich the picture of scientific enterprise, but also possess a special appealing power promoting genuine understanding of the concept considered. This approach draws on the historical tradition from Plutarch in distant past and Koyré in the recent history and philosophy of science. It gains a new support in the discipline–culture structuring of the physics curriculum, seeking cultural content knowledge (CCK) of the subject matter. Here, we address two prominent individuals of Italian Renaissance, Leonardo and Galileo, in their dealing with issues relevant for introductory science courses. Although both figures addressed similar subjects of scientific content, their products were essentially different. Considering this difference is educationally valuable, illustrating the meaning of what students presently learn in the content knowledge of mechanics, optics and astronomy, as well as the nature of science and scientific knowledge.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
In the general theory of relativity gravitation, all masses together determine the space–time curvature that determines the behavior of each individual mass.
In no way do I state that the suggested comparison between historical and individual conception excludes other strategies insisting on considering students’ conceptions. Such strategies are documented in the vast amount of other studies in recent three decades (e.g., Arons 1990). In the course of the article, I will mention the studies of students’ conceptions in order to illustrate the relevance of the specific subject matter and the certain similarity with students’ conceptions. This similarity provides strong motivation for the subject matter topics chosen here.
Moreover, historians who often have the intention to adequately represent the conceptual environment of a certain historical period, lacking some modern concepts and possibly using different terminology, may produce accounts inappropriate for using in contemporary science teaching.
This study does not pretend to contribute to the contemporary research discourse in history of science but only to draw on very specific subject matter and conceptual content from the past. The modern claim of science educators is that despite the very different concepts and understanding of the nature and framework of scientific knowledge, the views of the bright minds from the distant past may be useful for contemporary learners by establishing a space of concept variation (periphery in the cultural structure) in which students can construct modern scientific knowledge much more effectively.
The DC structure may be related to a scientific research program described by Lakatos (1970), which applied triadic code to describing a certain theoretical program. However, the codification of DC is different in contents.
In the pedagogical context, one may add students’ misconceptions to the periphery of a corresponding theory.
The use of the term “culture” is extremely wide. In anthropology, culture is defined as a space of all artifacts (Tylor 1871/1920, p. 1). Hofstede (1991, p. 5) emphasized in culture the features that distinguish between different clusters in that multitude. One of them—science—still allows for different aspects, such as ethnicity (Aikenhead 1997) and social interaction (Latour 1987). Redish (2010) emphasized culture of physics as a specific mode of thinking, behavior of scientists comprising hidden curriculum of epistemological and ontological nature. We followed another aspect that considers knowledge system as a culture of rules or texts (Lotman 2010). Within this perspective, cultural knowledge of science presumes representation that is explicit with regard to the conceptual difference between several fundamental theories showing family resemblance (Tseitlin and Galili 2005).
Stands for Galilei (1632/1953).
The inherent resistance to motion introduced by Kepler for celestial objects’ (instead of resistance to the change of motion) sometimes appears as a misconception of students (Galili and Tseitlin 2003). Newton explicitly denied it writing (Cohen 1971): “I do not mean Kepler’s force of inertia by which bodies tend toward rest, but the force of remaining in the same state whether of resting or of moving.”.
Stands for Galilei (1638/1914).
Galileo knew about Kepler's progress regarding elliptical orbits of planets and rejected it as he did regarding his idea of attraction at a distance (e.g. Drake 1999a, p. 342).
Thought experiment may show only what the theory chosen in it states, confirm, or reveal a contradiction in it. Galileo's thought experiment of falling objects showed the internal contradiction in the Aristotelian theory but could not suggest a new theory introduced later by Newton (Galili 2009).
In his criticism of Aristotle regarding falling, Galileo followed Hipparchus, Philoponus, Benedetti, and Stevin among others who observed the discrepancy of the Aristotelian account and experimented with falling (e.g., Dijksterhius 1970).
This was a remarkable recourse. In other cases (such as regarding pendulum isochronicity), Galileo showed quite a different attitude to the experiment, preferring convincing reasoning and considering an ideal case, free from impeding factors in actual experiment which may mask the "true" phenomenon.
As discussed in Lehavi and Galili (2009), Galileo's law of falling and the equivalence principle are often confused. While the latter is unconditional, the acceleration with which two masses approach each other—"falling"—depends on their masses. Two bodies of different masses approach each other ("falling") with relative acceleration that depends on their masses. In case of falling of regular ("small") objects to the ground, one may neglect the mass dependence (obtaining Galileo's law). However, in astrophysical context of comparable masses, Galileo's law does not hold. Revealing the approximate nature of Galileo's law may be used by teachers for demonstrating the importance of having a theory for the full account of phenomena. That cannot come solely from observation as cited from Galileo.
Using modern notifications, the distances covered by the sequentially dropped bodies \( S_{1} = 1/2gt^{2} \) and \( S_{2} = 1/2g(t - t_{0} )^{2} \) (t0 denotes time delay, g denotes free fall acceleration) yield for the separation: \( S_{1} - S_{2} \propto \; \, t \).
The sketches of Leonardo might suggest similarity with stroboscopic photos, but in fact they differ essentially. While Leonardo's sketches depicted the shape of the path and its perception by an observer, the stroboscopic photos would reveal segments of equal duration emphasizing the areas with the slowest speed of projectiles.
This knowledge is old. Aristotle used it as an example of the second type of inductive reasoning based on the specific regularity in Moon phases: The crescent Moon always faces the Sun with its convex side.
In his astronomical study Leonardo's depicted light sequential reflections from the Earth and Moon which allowed seeing the part of the Moon not directly illuminated by the Sun. The diagrams are located in Codex Arundel, fol. 28 r, and reproduced in Emanuelli 1956, p. 207.
This law was later rediscovered by Bouguer, the founder of photometry, in the eighteenth century (Wolf 1961, p. 167).
In his sketch of light reflection from the Moon Leonardo showed rippled surface which explained his identification of the bright areas on the Moon disk as “seas.” The sketch is located in Codex Arundel, fol. 25 r, and was reproduced in Emanuelli (1956, p. 206).
This view indicates Leonardo's belief that the Moon possesses its own atmosphere.
Common students' amazement accompanies demonstration of a black surface of an illuminated mirror (Galili & Hazan 2000).
Scheiner (1614) Disquisitiones Mathematicae, Ingolstadt.
Lacking a telescope Leonardo could not draw the lunar surface. There is speculation regarding Leonardo's telescope (Argentieri 1956, pp. 416–426), which, in any case, was never realized. Indeed, Leonardo's note looks suggestive: "…here [with the device] only one star is seen, but it will be large. Therefore, the Moon will be seen larger and its spots in a more defined form". (p. 422).
Leonardo's sketches of water stream passing obstacles and water shaft pouring into a pool are extremely accurate and faithful to reality in reproduction of the structure of turbulent motion. The sketches are located in Codex Windsor, fol. 12660 r, v and were reproduced, for example, in Zammattio (1974, p. 193).
The laws of photometry relate the illumination of a lit surface in the inverse square dependence with the distance to the light source (Bouguer’s law) and in direct proportion to the cosine of the angle of incidence of the light (Lambert’s law). This account presents a problem already in the school optics curriculum (Galili and Lavrik 1998).
In his sketch, Leonardo exposed creation of complex shadow by a circular screen and spherical light source. The sketch is located in Codex Atlanticus, fol. 187 r and was reproduced, for example, in Argentieri (1956, p. 413).
In that, Galileo corrected the argument of seasons by Copernicus (1543/1952, p. 530), who erroneously included the "third movement" of the Earth—the annual revolution of its axis westwards.
The amount of rays crossing the tablet is in direct proportion to the cosine of the angle between the normal to the plane and the direction of the light rays. This account presents a relevant problem in students' learning about illumination and season change (Galili & Lavrik 1998).
Leonardo's drawing of the self-supported wooden bridge is located in Codex Atlanticus, fol. 23 v-a, and was reproduced, for example, in Calvi (1956, p. 297).
The sketch of Leonardo's experiment of the loaded rod fixed at one end is located in Codex Atlanticus, fol. 211 r-b, and was reproduced, for example, in Uccelli (1956, p. 271).
This and other scaling arguments continue to serve researchers as a guiding method in paleontology in the interpretation of remnants of dinosaurs.
The picture is in opposition to stroboscopic pictures usually used in physics textbooks. A stroboscopic picture (Fig. 6b) shows more crowded locations at the extremes of the swing deviation, where the velocity of the bob is low. Leonardo makes denser images next to the lowest point of the swing, equilibrium point, where the velocity is the highest. In this way Leonardo seemingly wanted to show the swiftness of the bob—a creative trick with a great visual appeal, as it was usual for him.
In classical mechanics the claim of equal time descend along chords receives a simple proof at school physics class.
The problem of isochronicity was solved in 1673 by Huygens with the trajectory of cycloid. This curve was the true brachistochrone—the path of the quickest descent between any two given points. It was later proved by Leibniz, Newton and Bernoulli in 1697 (e.g., Matthews 2000, pp. 124–133).
Through chords Galileo approached the functional dependence of the pendulum period as proportional to the square root of its length but could not receive the coefficient 2π and failed to see the exact account in the limit of small angles providing isochronicity.
Two opposite historical cases illustrate this choice. The discovery of the neutrino is the first one. The violation of energy conservation in spontaneous nucleus decay was reported in the 1930s. It was addressed by two potential explanations. One imagined that energy conservation could not hold in the micro-world (Bohr), and another suspected a missed product (particle) of the beta decay (Pauli) that could save energy conservation (Fermi 1934). The actual discovery of neutrino took place much later, in the 1950s. The opposite case is even more famous. Facing zero result in Michelson–Morley experiment most of physicists tried "to save the phenomenon" by trying to explain it within the existed knowledge of physics (e.g., Miller 1981/1998, 1986). Einstein alone went the opposite way and caused the revolution in physics by his theory of relativity.
References
Aikenhead, G. S. (1997). Towards a first nations cross-cultural science and technology curriculum. Science Education, 81(2), 217–238.
Albert of Saxony. (1959). Questions on the four books of the heavens and the world of Aristotle. In M. Clagett (Ed.), The science of mechanics in the middle ages (pp. 565–567). Madison, WI: The University of Wisconsin Press.
Argentieri, D. (1956). Leonardo’s Optics. In E. Vollmer (Ed.), Leonardo da Vinci (pp. 405–436). New York: Reynal.
Ariotti, P. (1968). Galileo on the isochrony of the pendulum. Isis, 59(4), 414–426.
Arons, A. (1990). A guide to introductory physics teaching. New York: Wiley.
Atalay, B. (2004). Math and the Mona Lisa. Washington, DC: Smithsonian Books.
Bedini, A. S., & Reti, L. (1974). Horology. In L. Reti (Ed.), The unknown Leonardo (pp. 240–263). New York: McGraw-Hill.
Braga, M., Guerra, A., & Reis, J. C. (2012). The role of historical-philosophical controversies in teaching sciences: The debate between biot and ampere. Science & Education, 21, 921–934.
Burtt, E. A. (1927). Galileo’s method. The metaphysical foundations of modern physical science (pp. 64–73). Harcourt: Brace & Co.
Calvi, I. (1956). Military Engineering and Arms. In E. Vollmer (Ed.), Leonardo da Vinci (pp. 275–306). New York: Reynal.
Capra, F. (2007). The science of Leonardo. New York: Anchor Books.
Clagett, M. (1959). The science of mechanics in the middle ages (pp. 541–556). Madisson, WI: The University of Wisconsin Press.
Coelho, R. L. (2010). On the concept of force: How understanding its history can improve physics teaching. Science & Education, 19, 91–113.
Cohen, I. B. (1971). Introduction to Newton’s principia (p. XVI, 28). Cambridge: Cambridge University Press.
Cohen, I. B. (1993). A sense of history in science. Science & Education, 2(3), 251–277 (1950, American Journal of Physics, 18, 343–359).
Copernicus, N. (1543/1952). On the Revolutions of the Heavenly Spheres. Chicago, IL: Encyclopedia Britannica.
de Santillana, G. (1955). The crime of Galileo. Chicago, IL: The University of Chicago Press.
Dibner, B. (1974). Machines and weaponry. In L. Reti (Ed.), The unknown Leonardo (pp. 166–189). New York: McGraw-Hill.
Dijksterhius, E. J. (1970). Simon Stevin: Science in the Netherlands around 1600. The Hague: Martinus Nijhoff.
Dijksterhius, E. J. (1986). The mechanization of the world picture. Pythagoras to Newton. Princeton, NJ: Princeton University Press.
Drake, S. (1957). Discoveries and opinions of Galileo. New York: Doubleday & Company.
Drake, S. (1978). Galileo at work. New York: Dover.
Drake, S. (1999a). Kepler and Galileo. In Essays on Galileo and the history and philosophy of science, Vol. I. Toronto: University of Toronto Press.
Drake, S. (1999b). Galileo: Scientific method and philosophy of science. In Essays on Galileo and the history and philosophy of science, Vol. I. Toronto: University of Toronto Press.
Emanuelli, P. (1956). da Vinci’s Astronomy. In E. Vollmer (Ed.), Leonardo da Vinci (pp. 205–208). New York: Reynal.
Fermi, E. (1934). Versuch einer Theorie der & #x03B2;-Strhlen. I. Zeitschrift für Physik., 88, 161–177.
Finocchiaro, M. A. (1989). The Galileo affair, a documentary history. Berkeley, CA: University of California Press.
Galilei, G. (1590/1969). Memoranda on motion. In S. Drake & I. E. Frabkin (Eds.), Mechanics in sixteenth century Italy (pp. 378–387). Milwaukee, London: The University of Wisconsin Press Madison.
Galilei, G. (1590/1960). De Motu. In I. E. Drabkin & S. Drake (Eds.), On motion & On mechanics. Madison, WI: The University of Wisconsin Press.
Galilei, G. (1610/1989). The sidereal messenger. Chicago, IL: University of Chicago Press.
Galilei, G. (1613/1957). Second letter on sunspots. In S. Drake (Ed.), Discoveries and opinions of Galileo. New York: Doubleday.
Galilei, G. (1623/1957). The Assayer. In S. Drake (Ed.), Discoveries and opinions of Galileo. New York: Doubleday.
Galilei, G. (1632/1953). Dialogue concerning the two chief world systems—Ptolemaic and Copernican. Berkeley, CA: University of California Press.
Galilei, G. (1638/1914). Dialogue concerning two new sciences. New York: Dover.
Galili, I. (2001). Weight versus gravitational force: Historical and educational perspectives. International Journal of Science Education, 23(10), 1073–1093.
Galili, I. (2009). Thought experiment—Establishing conceptual meaning. Science & Education, 18(1), 1–23.
Galili, I. (2011). James Hannam: Gods philosophers: How the medieval world laid the foundations of modern science. Science & Education, 21(3), 415–422.
Galili, I. (2012). Promotion of content cultural knowledge through the use of the history and philosophy of science. Science & Education, 21(9), 1283–1316.
Galili, I. (2014). Teaching optics: A historico-philosophical perspective. In M. R. Matthews (Ed.), International handbook of research in history and philosophy for science and mathematics education (pp. 97–128). New York: Springer.
Galili, I., & Bar, V. (1992). Motion implies force. Where to expect vestiges of the misconception? International Journal of Science Education, 14(1), 63–81.
Galili, I., & Hazan, A. (2000). The influence of historically oriented course on students’ content knowledge in optics evaluated by means of facets-schemes analysis. Physics Education Research, American Journal of Physics, 68(7), S3–S15.
Galili, I., & Kaplan, D. (1997). Changing approach in teaching electromagnetism in a conceptually oriented introductory physics course. American Journal of Physics, 65(7), 657–668.
Galili, I., & Lavrik, V. (1998). Flux concept in learning about light. A critique of the present situation. Science Education, 82(5), 591–614.
Galili, I., & Lehavi, Y. (2003). The importance of weightlessness and tides in teaching gravitation. American Journal of Physics, 71(11), 1127–1135.
Galili, I., & Tseitlin, M. (2003). Newton’s first law: Text, translations, interpretations, and physics education. Science & Education, 12(1), 45–73.
Gauld, C. F. (1977). The role of history in the teaching of science. Australian Science Teachers Journal, 23(3), 47–52.
Gauld, C. F. (1991). History of science, individual development and science teaching. Research in Science Education, 21, 133–140.
Gauld, C. F. (2014). Using history to teach mechanics. In M. R. Matthews (Ed.), International handbook of research in history, philosophy and science teaching (pp. 57–95). New York: Springer.
Gibbs-Smith, C. (1978). The inventions of Leonardo da Vinci. New York: Charles Scribner’s Sons.
Gliozzi, M. (1965). Storia della Fisica, Ch. 3. Storia della Scienze, Vol. 2, Torino.
Hannam, J. (2009). Gods philosophers. How the medieval world laid the foundations of modern science. London: Icon Books.
Helden, A. V. (1989). Introduction. In G. Galilei (Ed.), (1610/1989), The sidereal messenger. Chicago, IL: The University of Chicago Press.
Hofstede, G. (1991). Cultures and organizations: Software of the mind. London: McGraw-Hill.
Holton, G. (2003). The project physics course, then and now. Science & Education, 12(8), 779–786.
Jacoby, B. A., & Spargo, P. E. (1989). Ptolemy revived. Interchange, 20(2), 33–53.
Kalman, K. S., & Adulls, M. W. (2003). Can an analysis of the contrast between pre-Galilean and Newtonian theoretical frameworks help students develop a scientific mindset? Science & Education, 12(8), 761–772.
Kemp, M. (2006). Leonardo da Vinci, the marvelous works of nature and man. Oxford: Oxford University Press.
Kofka, K. (1925). The growth of mind (p. 44). New York: Harcourt, Brace & Co.
Koyré, A. (1943a). Galileo and the scientific revolution of the seventeenth century. The philosophical review. Journal of the History of Ideas, 52(4), 333–348.
Koyré, A. (1943b). Galileo and Plato. Journal of the History of Ideas, 52(4), 400–428.
Koyré, A. (1968). Newton and descarets. In Newtonian studies (pp. 85–155). Chicago: University of Chicago Press.
Koyré, A. (1978). Galileo studies. Hassocks, Sussex: Harvester Press.
Kurrer, K.-E. (2008). The history of the theory of structures. From arch analysis to computational mechanics, Berlin, Germany
Lakatos, I. (1970). Falsification and the methodology of scientific research programmes. In I. Lakatos & A. Musgrave (Eds.), Criticism and the growth of knowledge (pp. 91–195). Cambridge: Cambridge University Press.
Latour, B. (1987). Science in action. Cambridge, MA: Harvard University Press.
Lattery, M. (2001). Thought experiments in physics education: A simple and practical example. Science & Education, 10(5), 485–492.
Lehavi, Y., & Galili, I. (2009). The status of Galileo’s law of free-fall and its implications for physics education. The American Journal of Physics, 77(5), 417–423.
Levrini, O., Bertozzi, E., Gagliardi, M., Grimellini-Tomasini, N., Pecori, B., Tasquier, G., & Galili, I. (2014). Meeting the discipline–culture framework of physics knowledge: An experiment in Italian secondary school. Science & Education, 23(9), 1701–1731.
Lima, F. M. S., & Arun, P. (2006). An accurate formula for the period of a simple pendulum oscillating beyond the small angle regime. American Journal of Physics, 74(10), 892.
Lindberg, D. C. (1962). The beginnings of the western science. Chicago, IL: The University of Chicago Press.
Losee, J. (1993). A historical introduction to the philosophy of science. Oxford: Oxford University Press.
Lotman, Y. (2010). The problem of learning culture as a typological characteristic. In What people learn. Collection of papers and notes (pp. 18–32). Rudomino Book Center, Moscow (in Russian).
MacCurdy, E. (Ed.). (1955). The notebooks of Leonardo da Vinci. New York: G. Brazilller.
Mach, E. (1883/1989). The science of mechanics, a critical and historical account of its development. La Salle, IL: The Open Court.
MacLachlan, J. (1997). Galileo Galilei. First physicist. New York: Oxford University Press.
Marcolongo, R. (1956). da Vinci’s mechanics. In E. Vollmer (Ed.), Leonardo da Vinci (pp. 483–492). New York: Reynal.
Marton, F., & Tsui, A. B. M. (2004). Classroom discourse and the space of learning. Mahwah, NJ: Lawrence Erlbaum.
Matthews, M. R. (1990). Ernst Mach and contemporary science education reforms. International Journal of Science Education, 12(3), 317–325.
Matthews, M. R. (1994). Science teaching, the role of history and philosophy of science. New York: Routledge.
Matthews, M. R. (2000). Time for science education. New York: Kluwer.
Matthews, M. R. (Ed.). (2014). International handbook of research in history and philosophy for science and mathematics education, three volumes. New York: Springer.
McAllister, J. (1996). The evidential significance of thought experiments in science. Studies in History and Philosophy of Science, 27(2), 233–250.
McCloskey, M. (1983a). Naïve Theories of motion. In D. Genter & A. L. Stevens (Eds.), Mental models (pp. 299–324). Hillsdale, NJ: Lawrence Erlbaum.
McCloskey, M. (1983b). Intuitive physics. Scientific American, 248(4), 122–130.
Miller, A. (1981/1998). Albert Einstein’s special theory of relativity: Emergence (1905) and early interpretation (1905–1911). New York: Addison-Wesley.
Miller, A. (1984). Imagery in scientific thought creating 20th-century physics. Boston: Birkhauser.
Miller, A. (1986). Frontiers of physics: 1900–1911. Boston: Birkhauser.
Miller, A. (1996). Insight of genius. Copernicus. New York: Springer.
Monk, M., & Osborne, J. (1997). Placing the history and philosophy of science on the curriculum: A Model for the development of pedagogy. Science Education, 81(4), 405–424.
Pascal, B. (1910). Of the geometrical spirit. In Blaise Pascal: Thoughts, letters, and minor works. The Harvard Classics, Vol. 48, Collier & Son https://en.wikisource.org/wiki/Blaise_Pascal/Minor_Works
Pederson, O., & Pihl, M. (1974). Early physics and astronomy. London: Macdonald & Janes.
Plutarch, (1989). Parallel lives, volume VII. Demosthenes and Cicero. Cambridge, MA: Alexander and Caesar, Loeb Classical Library, Harvard University Press.
Redish, E. F. (2010). Introducing students to the culture of physics: Explicating elements of the hidden curriculum. In Physics education research conference 2010 plenary talk arXiv:1008.0578 [physics.ed-ph]. doi:10.1063/1.3515245
Scheker, N., & Niedderer, H. (1996). Contrastive Teaching: A strategy to promote qualitative conceptual understanding of science. In D. F. Treagust, R. Duit, & B. I. Frazer (Eds.), Improving teaching and learning in science and mathematics (pp. 141–151). New York: Teachers College Press.
Schwartz, D. L., Chase, C. C., Oppezzo, M. A., & Chin, D. B. (2011). Practicing versus inventing with contrasting cases: The effects of telling first on learning and transfer. Journal of Educational Psychology, 103(4), 759–775.
Segre, M. (1991). In the wake of Galileo. New Brunswick, NJ: Rutgers University Press.
Sequeira, M., & Leite, L. (1991). Alternative conceptions and history of science in physics teacher education. Science Education, 75(1), 45–56.
Sharratt, M. (1994). Galileo decisive innovator. Oxford: Blackwell.
Stein, H., & Galili, I. (2014). The impact of operational definition of weight concept on students understanding of physical situations. International Journal of Research in Science and Mathematical Education,. doi:10.1007/s10763-014-9556-7.
Stein, H., Galili, I., & Schur, Y. (2015). Teaching new conceptual framework of weight and gravitation in the middle school. Journal of Research in Science Teaching,. doi:10.1002/tea.21238.
Stinner, A., & Williams, H. (1993). Conceptual change, history, and science stories. Interchange, 24(1&2), 87–103.
Tseitlin, M., & Galili, I. (2005). Physics teaching in the search for itself. Science & Education, 14, 235–261.
Tylor, E. (1871/1920). Primitive culture, Vol. 1. New York: J. P. Putnam’s Sons.
Uccelli, A. (1956). The Science of Structures. In E. Vollmer (Ed.), Leonardo da Vinci (pp. 261–274). New York: Reynal.
Vitoratos, E., & Sakkopoulos, S. (2015). The contribution of history and philosophy to the conceptual approach of Physics. Old and new puzzles. Review of Science, Mathematics and ICT Education, 9, 93–104.
Wallace, R. (1966). The world of Leonardo. Alexandria, VA: Time-Life.
Wandersee, J. H. (1986). Can the history of science help science educators anticipate students’ misconceptions? Journal of Research in Science Teaching, 23(7), 581–597.
Wandersee, J. H. (1990). On the value and use of the history of science in teaching today’s science: Constructing historical vignettes. In D. E. Herget (Ed.), More history and philosophy of science in science teaching (pp. 278–283). Talahassee: Florida State University.
Welch, W. W. (1973). Review of the research and evaluation program of Harvard project physics. Journal of Research in Science Teaching, 10(4), 365–378.
White, M. (2000). Leonardo the first scientist. London: Abacus.
Wolf, A. (1961). A history of science, technology & philosophy in the 18th century (Vol. 1). New York: Harper.
Zammattio, C. (1974). The Mechanics of Water and Stone. In L. Reti (Ed.), The unknown Leonardo (pp. 190–215). New York: McGraw-Hill.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Endnote
This article unfortunately lacks many sketches by Leonardo, Galileo and Steiner, which are mentioned in the text but which were not included for copyright reasons. Though the appealing power of the statements was thus significantly reduced, my hope is that science educators will use those sketches in their teaching and research discourse for their elucidating impact on our learning and appreciation of science making it pleasing.
Conflict of interest
The author declares no conflict of interest.
Rights and permissions
About this article
Cite this article
Galili, I. From Comparison Between Scientists to Gaining Cultural Scientific Knowledge. Sci & Educ 25, 115–145 (2016). https://doi.org/10.1007/s11191-015-9785-3
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11191-015-9785-3