Abstract
Michael Faraday is considered one of the greatest science lecturers in history. He popularized the Christmas Lectures as a format of science communication that has survived until today in the Royal Institution of Great Britain. Especially, his Chemical History of a Candle has become a classic of science communication that has inspired numerous approaches to science teaching. Science educators have appreciated the wealth of factual knowledge to be derived from working with the candle (knowing science). In light of a more recent philosophy of science education, which advocates for an increased focus on aspects of scientific inquiry (doing science) to balance a mere amassing of facts, this article undertakes to analyze Faraday’s lectures with regard to their potential benefits for teaching scientific inquiry. It does so by referring to a proven teaching unit from the Art of Teaching. This approach will be briefly introduced along with the teaching unit. Hermeneutic analysis of original sources and secondary literature will illustrate how Faraday’s lecture and his views on experimentation can inform an augmentation of the teaching unit. It will be shown that the strength of Faraday’s lectures does not lie in its epistemological virtues. A theoretical explanation for this finding is provided from instructional psychology. Concerning the hallmarks of contemporary science education, Faraday’s lecture still goes beyond a mere communication of facts. Adapted to the classroom, it can improve introductory science lessons exploiting the affective benefits to be gathered from performing easy-to-do and impressive-to-watch investigations.
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Notes
We are aware that providing sources in the German language raises the bar to further scholarly examination. Concerning the present example, Art of Teaching, unfortunately, is presented in only one English article (Berg 2004) and some translations can be found on their website (http://www.lehrkunst.ch/index-staging-lessons). We feel, however, that we must counterbalance a pending impression of Art of Teaching being free of educational theory or philosophy. For this reason, we add the German references to (a) sketch the theoretical horizon and tradition of this paradigm and to (b) give the interested reader the opportunity to locate relevant literature.
See, e.g., Chang (2011) for a wider discussion on how (and for which reasons) historical experiments have been used in research and teaching and for a distinction between historical replication, physical replication, and extension. He draws attention to the epistemological potentials of surprising or nowadays unknown outcomes of historical experiments which he calls complementary experiments as they can complement modern canonical knowledge (e.g., water does not necessarily boil at 100 °C—cf. superheating).
The admittedly increased demands on lesson time that this approach makes are conceded by proponents of the Art of Teaching, and they estimate that approximately 10% of the curriculum should be delivered in this approach (Berg 2004).
We know that this simplistic view has been contested repeatedly with regard to inquiry teaching (e.g., Abrahams and Millar 2008; Hodson 1996). In this context, however, we would like to highlight the motivational dimension (i.e., intrinsically motivated, meaningful learning) inherent in the proverb’s claim rather than accounting for the cognitive challenges.
We are indebted to the IET’s archivist, Ms. Asha Gage, for retrieving this information.
These need to be distinguished from the renowned lectures given to an academic audience on occasion of an award ceremony such as the Royal Society of Chemistry’s Faraday Lectureship Prize that has been awarded since 1869.
Please refer to Appendix I to get a more detailed impression of Christmas Lectures in Faraday’s days.
For the remainder of the manuscript, the italicized Lecture refers to the original lecture series; the italicized Candle will denote reference to the Art of Teaching’s teaching unit (see Section 6).
Why he addresses only the boys regarding experimentation, although there must have been girls and women present (Faraday 1861, pp. 2, 142), must be left to speculation.
From Greek ἐνκύκλιος παιδείᾱ: general education, general course of education (Oxford English Dictionary; http://www.oed.com)
Hypotheses are, after all, only a mental construct, i.e. a creative artifact of the mind which is fallible on principle. Isaac Newton famously expressed his disdain against this non-empiricist nature of the hypothesis by claiming “Hypotheses non fingo.” (“I feign no hypotheses”; Newton 1713; p. 484).
“Didaktik,” here, is purposefully translated as an approach to teaching rather than as “didactics.” “Didactics” carries a derogatory connotation of indoctrination (Fischler 2011) which does not respect the students’ view. This does not reflect, however, its common German interpretation. “Art of Teaching” here must not be confused with Highet’s (1950/1956) understanding of the term, which sketches a wider, more general conditional network of quality teaching (e.g., teacher personal traits, principles of teaching, relating with students, etc.).
Art of Teaching relies on Klafki’s concept of the term, which understands Bildung not as something that is conveyed by teachers, nor acquired by students (as in a business deal), but as a developing character forming personal disposition. “Bildung is understood as a qualification for reasonable self-determination, which presupposes and includes emancipation from determination by others. It is a qualification for autonomy, for freedom for individual thought, and for individual moral decisions. Precisely because of this, creative self-activity is the central form in which the process of Bildung is carried out.” (Klafki 2000, p. 87)
Neither is there a pressing need to differentiate between invisible nitrogen and invisible oxygen regarding invisible air. Wagenschein is skeptical of too early an introduction of technical language as “term dropping” oftentimes obscures an underlying substantial lack of understanding. How many young students do enthusiastically use terms such as atom, molecule, and photosynthesis and how many of those really do understand the concepts?
While some aspects of the modus operandi of the Art of Teaching are reminiscent of Design-Based Research (iterative design-redesign cycles), we know of no comparable approach to teaching. The Art of Teaching suggests to treat teaching units like pieces of drama: Compose them, publish them, put them to the stage with “artistic license,” and improve from what you have learned—let always others use your script, too. Unlike in other creative fields of work (e.g., carpentry, painting, cooking), expert teaching is hardly disseminated in teaching studies and is guarded almost “jealously” by its creators. The Art of Teaching suggests taking “the other road.” Coupled with attendance to Wagenschein’s teaching principles of science education and to Klafki’s seminal theory of Bildung makes this approach unique to our knowledge.
Please refer to Appendix II to get a more detailed impression of the teaching unit.
“Faraday’s method of inquiry informs our composition of good reports. […] Anna: ‘Where do we put our questions and ideas?’ – Teacher: ‘When your ideas or questions exactly match your investigation, you put them under your observations.’” (pp. 125–126, our translation)
In this respect, the Art of Teaching appears to be an advocate for discovery learning rather than for inquiry learning (cf. French 2006; Prince and Felder 2006, 2007). Pure discovery learning approaches have been shown to be ineffective (e.g., Mayer 2004) and learning might benefit from guidance and scaffolds as offered in inquiry learning (e.g., Bell et al. 2005).
The focal term in this context is “re-cognize.” The word already signifies that something comes back to knowing; it can be traced back to Latin recognoscere, “to know again.” So, observation in experimentation does not mean to know anew. In 1854, Louis Pasteur rightly remarked “Dans le champs de l’observation le hasard ne favorise que les esprits préparés.“ (“In the field of observation fortune favours only the prepared mind.” (Gillies 2006, p. 54))
One might be reminded of Maslow’s Law, the Law of Instrument respectively, here: “I suppose it is tempting, if the only tool you have is a hammer, to treat everything as if it were a nail.“(Maslow 1966, p. 15)
Justus von Liebig draws attention to experience’s influence on the economy of experimentation: “[…] an experienced man conducts far fewer investigations than an unexperienced one who must acquaint himself with many of the phenomena, that the former is already familiar with. For achieving several aims, often investigation will appear dispensable to the former as a combination of already known processes or facts will suffice.” (our translation of: „[…] ein erfahrener Mann macht viel weniger Versuche als ein unerfahrener, der sich mit vielen Erscheinungen erst bekannt machen muß, die dem andern bereits geläufig sind, und für die Erreichung vieler Zwecke sind dem ersteren häufig Versuche überflüssig, da die Combination der ihm bekannten Vorgänge oder Thatsachen dazu ausreicht.“(Liebig von Liebig 1865, p. 22))
This does not mean that research could not originate in surprise findings. In these cases – ‘troublesome discoveries’ as Kuhn (1962) terms them – there still is some expectation as to the outcome of an experiment and it is the violation of the expectation that brings about the discovery. Fleming (of Penicillin fame) allegedly commented on his moldy petri dish “That’s funny.” because he realized that something different was at play than a mere negligence of lab hygiene. It is this special awareness towards the out-of-the-ordinary that is decisive (Gillies 2006), at the same time, it is telling of preformed concepts and expectations.
Should the reader now object that a choke always needs to be pulled, they may be encouraged to reflect on how they know this and if (and why) younger readers might possibly be not familiar with the concept.
We are aware that Greek HiFi-equipment usually is labeled in the Latin alphabet using POWER or STANDBY. For the sake of argument, we fictionalize in this instance the product of a proud, language-sensitive Greek manufacturer who insists on labeling in his mother tongue.
Faraday says “I pour some water containing a little acid (but which is put only for the purpose of facilitating the action, it undergoes no change in the process) […]” (p. 90) because he knows—as a fact before putting his procedure into action—that without an increase of ionic substance (i.e., dissociated acid molecules) the conduction would be very bad and, thus, electrolysis would be hindered since water is “one of the worst as to its capability of facilitating conduction and suffering decomposition” (Faraday 1833/Faraday 1859, p. 123).
In Wagenschein’s words, the Candle wants to “save the phenomena” and thus to give immediate perception priority over scientific abstraction. “In the same way in which a children’s hospital, hygienic though it may be, cannot replace the mother in early childhood, in basic physics education the natural phenomenon cannot be represented by quantitative laboratory effects, however exact they may be, and this goes even more strongly for representing phenomena by means of models.
Physics will appear to the learner other than what it is – not a mindscape that limits but illuminates, overarching original nature and enriching it, but rather a subject that throws a shadow over an eerie Natura denaturata (denatured nature) and makes it desolate.” (Wagenschein 2008, n. p.)
From the Royal Institution’s advert in the London Times from December 1825. Quoted from a photograph on the Royal Institution’s interactive timeline (https://www.rigb.org/our-history/timeline-of-the-ri. Accessed 13 January 2020).
According to the National Archives’ Currency converter (http://www.nationalarchives.gov.uk/currency-converter/. Accessed January 14 2020), one guinea of 1860, i.e., 1 pound and 1 shilling, was equivalent to five work-day wages of a skilled tradesman or to 62 ₤ (73 €) in 2017. The Bank of England’s Inflation calculator (https://www.bankofengland.co.uk/monetary-policy/inflation/inflation-calculator. Accessed 14 January 2020) even gives an approximate equivalent of 120 ₤ (142 €) in 2018.
https://www.rigb.org/our-history/people/a/charles-anderson (Accessed 14 January 2020)
In contrast, Faraday devotes his complete third lecture to water, dedicates lecture V largely to carbon dioxide and oxygen spending roughly one lecture (IV) on hydrogen.
We are referring to these practical exercises here as “experiments” in its intuitive and imprecise understanding with which it is to be found in science textbooks for school, i.e. “hands-on” equals “experiment.” We do not consider the exercises to be experiments in a strict sense, as they are not deliberate, variable-controlled investigations of cause-effect relationships in natural phenomena (cf. Section 3 in the main manuscript). As intimated earlier in appendix II, these exercises might qualify more as observations.
This eventually (and almost inevitably) leads to a “contest” of whose flame can travel the farthest. For this, students must realize what they have to do to increase the traveling distance and then verbalize this. Again, observation comes very much into play.
The physics-related aspects can—to a large degree—feed from the children’s familiarity with candles and their play with birthday candles or the Advent wreath.
πυ̑ρ, fire; λύσις, dissolution (Woodhouse 1910)
φω̑ς, light; σύνθεσις, combination (Woodhouse 1910)
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The present article is the byproduct of a presentation given at a Summer School in Hamburg in 2019. One of the authors was invited to give his analysis of a science education teaching unit dealing with Faraday’s famed Candle-lectures. The teaching unit has been in constant development since the 1990s and has successfully been brought to numerous science classes in Germany and Switzerland (cf. Theophel 1995; Wildhirt et al. 2004; Wildhirt 2008).
Appendices
This appendix is based largely on the various reports for the teaching unit that can be found in Wildhirt et al. (Wildhirt et al. 2004) and in Wildhirt (2008). Additionally, some unpublished personal experience in teaching the unit is incorporated.
Appendix I Michael Faraday: The Chemical History of a Candle (1860/1861)—A Series of Six Lectures Held at the Royal Institution of Great Britain
As described in this manuscript’s main body, the Christmas Lectures were introduced to the Royal Institution in the mid-1820s. They were part of a strategy to increase the visibility of what the Royal Institution was doing (James 2007). Originally, it was intended to provide “that a Course of Lectures should be delivered at the Royal Institution, in the Christmas, and other vacations, on some of the leading branches of Natural Philosophy adapted to the comprehension of a juvenile audience [i.e. 15- to 20-year-olds]”.Footnote 27 Yet, it was only the Christmas series that were taken up favorably and, thus, these were the only ones to be continued.
Faraday did not contribute the first of these series—this was done by John Millington performing a “tour de force” of contemporary physics covering aspects from dynamics, mechanics, pneumatics, hydrostatics, optics, magnetism, electricity, and astronomy27. Faraday gave his debut in 1827 delivering 19 lecture series in total until he bade his farewell with the Candle in 1860. Neither Faraday nor his wife were comfortable with him giving this lecture as Faraday was too aware of his waning memory and was afraid of doing the lecture a disservice by this (Faraday 2011). Yet, the original choice for that season’s Christmas Lecture, John Barlow, had to resign for reasons of poor health and, thus, the Royal Institution was in dire need of a substitute lecturer (Faraday 2011).
Faraday relied on his notes for this lecture series as he had presented it in the 1848/1849 season. Fortunately, he could be convinced to step in for Barlow and, luckily, he relied on his earlier lectures. Otherwise, the lecture series might have been lost for good. Faraday had not consented to it being recorded by shorthand before he learned of the success of the publication of the previous season’s The Various Forces of Matter and Their Relations to Each Other (Faraday 2011; James 2007).
The lecture series was presented on six days beginning just after Christmas and continuing into the New Year. Viewers were charged one guinea for the complete course of six lectures (i.e., 21 shillings or 1.05 ₤ in modern terms; the guinea had ceased to be legal tender around 1816 but maintained to be a popular reference) for adults (non-members), half a guinea for under-16-year-olds (The Athenæum, No. 1730, December 22, 1860).Footnote 28 Lectures would start at 3 pm and probably last for an hour (Lan and Lim 2001) as Faraday disapproved of longer lectures (James 2002). The auditorium at the Royal Institution could hold more than 1000 viewers (James 2007), but as hinted in the article, somewhat short of 700 visitors attended on average (Faraday 2011). These would have experienced Michael Faraday addressing them on matters of the candle. He would be assisted in the demonstrations and experiments by Charles Anderson, who had been a lecture and laboratory assistant from 1832. He had come to the Royal Institution in 1827 to work with FaradayFootnote 29 and was 70 years old by the time of Faraday’s final lectures.
A famous painting by Alexander Blaikley (1816–1903, Fig. 1) shows us Faraday standing behind a work bench on which several of his demonstrations are prepared. He is standing, reading from his notes. Behind his right shoulder (probably) Charles Anderson is waiting for his cue to start the demonstrations. The auditorium is “packed”—curiously, with more adults than young people but this might have been either artistic license or have been due to the Prince of Wales’s presence at the said lecture (cf. James 2011). The usual tally of “unaccompanied adults” usually did not exceed 15% (Forgan 1977, p. 191). The painting has served as the source for the design of the British 20 ₤-note from series E that was in circulation from 1991 to 2001.
Alexander Blaikley’s painting of Faraday giving the 1855 Christmas Lecture in Attendance of the Prince of Wales (https://commons.wikimedia.org/wiki/File:Faraday_Michael_Christmas_lecture.jpg (in the public domain))
Faraday would develop his thoughts on a topic in a narrative fashion as he was quite aware of the differences between being read and being listened to—he had developed his personal style for lecturing early in his career, he had trained and perfected it with his friend Benjamin Abbott (Kauffman 1996; Lan and Lim 2001; James 2002). He “seasoned” his observations and explanations with scientific illustrations as he was deeply skeptical of dogmatic instruction that was not supported by the senses: “If […] I said to my audience, ‘this stone will fall to the ground if I open my hand,’ I should open my hand and let it fall. Take nothing for granted as known; inform the eye at the same time as you address the ear” (Reeve 1863, p. 152). The demonstrations could be very easy and small ones such as his “very pretty, but very common-place experiment” (Faraday 1861, p. 19) to reignite the rising vapor from a freshly blown-out candle. Yet, they could also be very complex and difficult to understand such as his apparatus to decompose water into hydrogen and oxygen (Faraday 1861, p. 70), which consisted of a boiler and a reaction tube filled with iron filings that were made red-hot. Although his audience could hardly have been in a position to intuitively follow the latter of these two examples, he made sure to build up toward this experiment. Before producing hydrogen and oxygen, e.g., Faraday showed his audience that steam will contract when cooled down so that they should not assume that steam had been produced in the reaction tube.
He appears to have expected no prior knowledge of his audience apart from an awareness of everyday observations. Every piece of additional information is presented and well argued; Faraday’s listeners were not expected to believe at face-value or accept it because famed Dr. Faraday had said so; he wanted them to see and realize for themselves. His onlookers will not have left the lecture feeling tricked or run over. They might have felt overwhelmed, which could easily be attributed to the sheer amount of scientific knowledge they had been exposed to for the preceding hour.
Many of his demonstrations (subsequently, all quoted from Faraday 1861) have gone into the “public domain” and are often conducted even with young children, e.g., producing soot from the flame (pp. 42), showing capillary attraction with a towel (pp. 14), implosion of a steam-filled vessel on cooling (pp. 63), and expansion of water on freezing (pp. 62). Many of these have found their way into the standard repertoire of science classes and are—to a modern-day audience—quite familiar. Others, again, are met less frequently, even if they are considerably easy to realize, e.g., showing the shadow a flame casts in back projection and the ascending air flow (pp. 5) and collecting water from a burning candle (pp. 55). Others again, could not be employed in school classes nowadays for making use of hazardous chemicals, e.g., burning of white phosphorous (p. 46) and using nitric oxide to test for oxygen (pp 112).
If Szydło’s (2017) count of experiments is to be trusted (he gives no source), we are led to assume that the total tally of experiments in the run of Faraday’s Six Lectures on the Chemical History of a Candle could easily come close to 200. In other terms, roughly each 2 min of the lecture series, Faraday’s audience was provided with sensory stimulus and evidence of the surrounding science in a demonstration—too many for teaching purposes but great for science communication, i.e., Victorian Edutainment.
Appendix II The Art of Teaching: Faraday’s Candle—A Teaching Unit for Introductory Science Classes (Mostly) at the Secondary Level
This appendix is based largely on the various reports for the teaching unit that can be found in Wildhirt et al. (Wildhirt et al. 2004) and in Wildhirt (2008). Additionally, some unpublished personal experience in teaching the unit is incorporated.
Faraday’s Christmas Lectures and the Art of Teaching’s classroom translation strive for different aims. Faraday was a science communicator—in his Christmas Lectures at least—and wanted to beat the drum for science. He probably did not have in mind to make his listeners become proficient scientists. For this reason, he could and had to adopt a faster paced way of delivering his lecture (an experiment every 2 min!). Science education, on the other hand, wants students to understand science and to learn to do it themselves. This demands more attention to detail and, thus, requires the science teacher to devote larger portions of lesson time to dealing with experiments. It is for this reason that the Art of Teaching approach to Faraday’s Candle has focused mainly on aspects from two lectures in the series instead of recreating the full experience.
Students in the Art of Teaching’s approach investigate the Candle without also spending much of their time on characterizing the products of combustion—they are identified by analytical tests but apart from this, their properties are not of the essence.Footnote 31 Students are meant to learn to observe and to describe, ideally to find answers to their own questions. For this reason, the teaching unit adopts mostly those experiments from Faraday’s lectures that students can conduct on their own and which are easy to see or to understand—there is no lengthy discussion of how nitric oxide can be used to test for oxygen (a discussion that needs an alert mind with the trained chemistry teacher already). Ideally, each student can work with their own candle and come to realize the small wonders in this allegedly trivial artifact.
The Art of Teaching’s Candle, however, preserves and extends one of Faraday’s “byproducts.” The candle is a perfect exemplar to introduce the idea of natural cycles, namely the carbon cycle (Lecture VI). The Art of Teaching hinges its unit on this idea by creating a trivial sounding but truly gravitating question: Where does a candle go to? Where does it come from?
Students “philosophize” on these questions sitting in front of four burning bees wax candles (each having burnt to different heights). While they are speculating about and reconstructing the where-from, the smallest of the candles expires forcing the where-to on the students. This introduction to the unit usually takes a full period (45 min). This extended discussion engages students in the topic and virtually draws them into the unit. If this fate of the candle was to be provided in an expository fashion, students could not develop an open and intrigued mindset toward the related questions. After this lesson, students are keen on finding out and learning about the candle. In a next step, the teacher encourages them to draw a candle flame from memory, which is no easy feat at all: which is its shape, which are its colors, and wasn’t there some darker portion inside it? After this, they compare their drawings with an actual candle flame and will realize where their memories have “failed” them or—simply—what they have never observed before, as opposed to having seen flames uncounted times before. The latter is predominantly physiological registration, the former is an act of cognition—this exercise is, thus, their first lesson in scientific epistemology.
Michael Faraday is then introduced as a famous scientist who had to say much on the candle and who can help the students answering their questions. Students are introduced to the Christmas Lectures and that even then children as old as themselves were intrigued to learn about the candle by no other than Michael Faraday. Faraday will assist the students in the following lessons; he will read relevant passages from his own lecture notes—Faraday, of course, is the teacher who will don some sort of disguise or signifier when slipping into Faraday’s persona (e.g., a bow-tie, a lab coat, or reading glasses). This kind of role-play is essential for the teaching unit and one of the authors, who has taught Faraday’s Candle bilingually, is happy to report that students who were rather shy to contribute to his English lessons suddenly felt remarkably at ease addressing “their” Michael Faraday in their second, far-from-perfect tongue.
The approximately 20 periods (of 45 min each) that follow are delivered in similar structure: Core of the lesson are one or two of Faraday’s demonstrations (see Table 1 in the main body of the article). Students are, wherever possible, equipped with the necessary apparatus to conduct the “experiments,”Footnote 32 i.e., a candle, glass tubes, wire gauze, beakers, etc. They are then introduced by “Faraday” to a specific phenomenon which they are encouraged to reproduce. Thus, students learn letting the flame travel themselves (the “beautiful but common-place experiment” of Faraday’s).Footnote 33 After having watched and cherished the phenomenon for some time, the class is given the scientific background knowledge by Faraday (again, quoting from his lecture notes where possible). In other instances, it might be feasible to arrive with students at a solution by Socratic talk—they will, e.g., realize that the vapor rising from the wick in the traveling flame experiment needs to be some ignitable and combustible substance, which will most often lead them to speculate that it might be the candle’s wax. Going from there, they might ask where the vaporized wax comes from and where it does “reside” in the candle, its flame respectively. “Faraday” then will search together with them for something that can cut a window into the flame, i.e., the wire gauze. In this respect, the Lecture provides a good model to base the argument of the teaching unit’s narrative on.
In this way, students experience many of the physical phenomena of the candle firsthand. The sequence of demonstrations in the teaching unit has been changed from Faraday’s original to account for the teaching unit’s narrative. Thus, the physical properties of the candle are well separated from its chemical and biological aspects. Some of the experiences must be made “second hand” as only the teacher—or better still “Faraday”—can show them for safety reasons. Having fireworks by mounting a burner horizontally and sprinkling iron filings, copper dust, or soot into the flames cannot be accomplished in eight-student workstations at once. The ignition of wax that has been heated until vapor rise cannot be left with inexperienced students. However, they must not be denied the spectacle, either. The latter portion of the unit, i.e., chemical aspects, tend to be more teacher-centered as students can hardly rely on prior knowledge.Footnote 34
Students record all the demonstrations, questions, and explanations in their folders—for some students a “backward organizer” has been issued. In contrast to the more familiar concept of the advance organizer, this is a pictorial mnemonic that summarizes the complete unit from its gravitational question to its resolution (Fig. 2). Starting with the burning candles (left hand side), running clockwise through the collection of water from the flame, and testing for carbon dioxide, a flowering meadow (right) is depicted from which bees collect pollen and nectar to eventually build their honeycomb and cover it with wax, which then can be made into new candles. Crucial terms and ideas are noted, two of these being pyrolysis and photosynthesis. In the unit, both these terms derive from intuitive (i.e., mother-tongue) descriptions of their designated processes; the flame’s fire separates the wax’s elements (fire separation)Footnote 35 and light combines these (light combination).Footnote 36 Only after these own terms have been “invented,” does “Faraday” introduce the technical terms (cf. Wagenschein 2008).
Mnemonic poster for the teaching unit of Faraday’s Candle (courtesy of S. Wildhirt)
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Emden, M., Gerwig, M. Can Faraday's The Chemical History of a Candle Inform the Teaching of Experimentation?. Sci & Educ 29, 589–616 (2020). https://doi.org/10.1007/s11191-020-00119-5
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DOI: https://doi.org/10.1007/s11191-020-00119-5