The moon and its movement
The moon and its movement is a genetic course of Martin Wagenschein's 1953, consisting of several examples , on the kinetics of the moon , which in particular reveals Isaac Newton's law of gravitation . He builds on Wagenschein's example The Law of Fall in the Fountain Beam , which Galileo Galileo's Law of Fall has as its theme, and generalizes it to objects that are not near the surface of the earth. In particular, Newton broke through the notion that has existed since time immemorial, also explicitly and vehemently advocated by Aristotle , that “in heavenly” other laws apply than on earth.
Wagenschein's example appeared in 1953, together with the law of fall in the fountain beam , in his much-acclaimed book Nature seen physically . Six years later , educational didactic specialist Wolfgang Klafki , who became known in 1957 with an epoch-making dissertation on categorical education , was explicitly published in his essay Categorical Education. For the educational theory interpretation of modern didactics. discussed as a good example of categorical education and is the basis for a piece of teaching art didactics .
Wagenschein's book The Earth under the Stars. A path to the stars for each of us. from 1955, which takes up many aspects again and is the template for the didactic piece Eratosthenes' Celestial Clock .
History of origin
Wagenschein's course on the movement of the moon was created only a few years after the Tübingen conversation in 1951, in which it was criticized that the students were exposed to a flood of material, but that this did not give them the opportunity to penetrate "really important" content with examples . In particular, the question of why the moon does not fall is a typical archetypal question that Wagenschein would like to see treated more genetically and genetically .
content
construction
Wagenschein's course is a bit unorthodox. He numbers his brief preliminary considerations with 1 to 4 , in order to then set up initial theses in points 5.1 to 5.3 , expand them step by step in 5.4 to 5.19 and take stock in 5.20 to 5.24 . A total of ten hand drawings illustrate his basic ideas and arguments.
Started
The essay opens with three quotes from Johann Heinrich Pestalozzi , Ernst Mach and finally Werner Heisenberg :
“Today we can hardly imagine what an extraordinary experience it must have been for researchers of that time to recognize that the movements of the stars and the movements of bodies on earth are traced back to one and the same simple system of laws can; whoever has not felt a little of the significance of this miracle can never hope to understand something of the spirit of modern science. "
Wagenschein stated that the young man of to learn to see the moon as a small ball that umfliege the earth in a circular orbit, this theoretical body early but nothing with the moon of his nights and poems have to do, leading to uprooting lead :
"Isn't that the barbarism of knowledge, the splitting of the person into a knowing but dead half and a secret, believing, childlike, livelier half, forcibly separated from the other?"
In contrast, he suggests that the “inner contact with the subject of reflection and calculation” should be cautiously taken up and at the same time that the topic should be introduced as an “introduction to the mathematical and scientific way of thinking”.
With quotes from Xenophanes (around 570 BC - around 470 BC), Heraklit (around 520 BC - around 460 BC), Parmenides (around 520/515 BC - around 460 / 455 BC), Anaxagoras (around 499 BC - 428 BC) and Plato (428/427 BC - 348/347 BC) he proves that humanity or The great minds of the ancient Greeks had only come to the realization in many difficult stages that the moon is a celestial body that is illuminated by the sun and, compared to it, much closer, celestial body.
Geometry of the moon movement
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After the introductory theses and considerations, Martin Wagenschein first devotes himself to the geometrical properties of the moon's motion, which can be measured from Earth, which also includes distances, absolute values and ultimately the orbital speed.
He begins with a view of the narrow crescent moon next to the setting sun as the moon is waxing and suggests that the moon is illuminated “from behind”, and that the sun must therefore be considerably further away than the moon. If the distances did not differ significantly from one another, we would see exactly the half of the moon facing the sun illuminated. However, since the sun and moon appear almost exactly the same size from the earth, it already follows that the sun must also be many times larger.
Now follows a calculation by Aristarchus of Samos from about 264 BC: With an exact half moon, he measured the angle between the sun and moon. While Aristarchus, with his possibilities at that time, still reached an angle of 87 °, we now know that this angle of 89 ° 51 'is much closer to the right angle. If one came from Aristarchus' value via the reciprocal value of the cosine to the factor 19, the more exact value would lead to the factor 382, with even greater accuracy the known factor 400 would be quite good. The sun is 400 times as far away and 400 - times the size of the moon.
After the size and distance relationships have been clarified, Wagenschein devotes himself to determining the actual distance of the moon from the earth. Here he draws on a historical measurement by Jérôme Lalande and Nicolas-Louis de Lacaille from February 23, 1752:
Lalande in Berlin and Lacaille in Cape Town measured the elevation angle of the moon exactly at the zenith. Since both cities are on the same longitude, but differ by 86.5 ° in latitude, the distance to the moon can be determined from the known earth radius of 6370 km. Lalandes α = 57 ° 55 'in Berlin and Lacailles β = 34 ° 17' at the cape, added to the 86.5 ° at the center of the earth, to a residual angle of 1.3 °. To get over the sinus applied to one half of the isosceles triangle between Earth's center, and two cities, on a linear distance between Berlin and Cape Town from 8,729 kilometers and on the law of sines to a distance of the moon to Berlin of around 375,680 kilometers. Using the cosine law, this results in a distance of the moon from the center of the earth of almost 381,100 km, which corresponds to 60 earth radii. Wagenschein does not carry out the calculations explicitly and does not refer to the relevant sentences, but rather shows the constructability of an exact scale drawing and then gives the literature value of 382,200 km.
Finally, at the end of the geometric part, Wagenschein asks about the size of the moon, which can now be determined using the ray theorems. A plate with a diameter of 7 cm, which can darken the moon 8 m away, leads to a moon diameter of 3,346 km. Martin Wagenschein avoids mentioning that the two numerical values for the plate by arctangent , applied to the corresponding half-triangle, can also be used to calculate the angle that the moon makes in front of our eyes of almost exactly half a degree. As a rough value he records "about a quarter of the earth's diameter" for the diameter of the moon and 100 times the diameter of the earth for the sun's diameter.
The same forces as on earth?
After the geometric data (he himself speaks of the "order of space") have been secured, Wagenschein now lets the moon take shape and recommends looking through a telescope to convince himself of the moon's spherical shape. However, he already sees a still latently smoldering problem with the learner, to accept the earth's own rotation as such, which allows us to observe the moon's movement only relative to it. He refers to old objections of Tycho Brahe and Giovanni Riccioli , which he often heard from children, in particular to the thesis that falling objects “would have to fly west” .
The orbital speed can be calculated quite easily using the circumference of the circle, if you realize that the moon needs a sidereal month, 27.32 days, to orbit the earth; it is around one kilometer per second, i.e. around 3,600 kilometers per hour. The childish question of why the moon is circling at all, however, remains for the student who, according to Wagenschein's guess, only felt “his astonishment calmed down” “if he saw a taut rope lead to the moon that would hold it” .
After the pioneers Nikolaus Kopernikus (1473–1543), Johannes Kepler (1571–1630) and Galileo Galilei (1564–1642) it was only Isaac Newton (1643–1727) who asked the basic question of whether the stars really comply with the “earthly” laws obeyed, could satisfactorily affirm. Newton's idea was to imagine the moon or a stone thrown from an extremely high mountain: If the speed of fall was slow, the stone, obeying Galileo's law of fall, would have to assume a parabolic path. If you now increase the throwing speed, the stone would not only fly “forward”, but at some point would also partially circle the earth. And it increased the initial rate even more, its tangential movement would eventually as strong as its "Fallen" and he would be on the top of the mountain again exactly as fast as he would have been thrown - he fall , so to speak "around the Earth" .
After this model has been dealt with as “possible”, Wagenschein invites critical doubts. He admits that no earth's atmosphere slows the moon on its way, without much counter-argument, to the moon at a distance of 60 earth radii. In order not to make things too easy for the learner, however, he postulates that the moon must fall just as low as a thrown or falling stone, in short time intervals and relative to the earth. And according to the laws of fall, such a device would fall 5 m deep in one second, which Wagenschein describes as the “identification mark” of the earth's gravity.
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However, geometrical considerations about the moon's movement with known orbital speed show that the moon only moves 1.35 mm towards the earth within five seconds. This would at least mean that the gravitational pull of the earth would rapidly decrease in the distance. Wagenschein considers the propagation of sound and light in the room: Both thin out the further they move away from the pathogen. After the spherical propagation, sound is distributed over four times the spherical surface at a distance of two meters as it is at a distance of one meter. If such a spread is also present with gravitation, it should have already sunk to a quarter in one earth radius away from the earth's surface and with 60 earth radii, which corresponds to the distance to the moon, to its 3,600th part. And this is exactly the 1.35 mm in relation to the 4.905 meters fall distance per second near the earth. On the one hand, a law about the decrease in gravity with distance seems to have been found and confirmed after measurement and calculation, and on the other, Newton's basic thesis, the moon is held on its path by "earthly" forces, found to be more than tenable.
Wagenschein closes his course with a look at Kepler's previous achievement, once again emphasizes the real advantages of a genetic approach and also explains why he did not calculate exactly or even infinitesimally everywhere here .
"It should be shown:
1. How it seems possible with a very small amount of mathematical knowledge (ray theorem, Pythagoras) and other physical knowledge (law of fall) to give an insight into the mathematical-scientific method using an example that is in the Western intellectual history made an epoch.
2. That such insight only life and depth to win (and then also reserves) when on a careful foundation has eight of all concepts and terms used in such a way that they remain in close conjunction with the in nature experienced.
3. That a less modest introduction to the system of Newtonian mechanics (which included Newtonian principles, the equation force = mass times acceleration, the centripetal formula and the basic terms of calculus) is not relieved of this experience-like foundation . "
Discussion by Klafki
In Wolfgang Klafki's essay Categorical Education. For the educational theory interpretation of modern didactics. 1959 Wagenschein example has the genetic development of the circular path to Newton a key role in the illustration of his thesis, real categorical education find place only when all four then current educational theories alike interact to opening up and Urban are conducted:
"We call education that phenomenon in which we - in our own experience or in the understanding of other people - become immediately aware of the unity of an objective (material) and a subjective (formal) moment."
Klafki gives Wagenschein's topic a "meaning of life" and writes of a "joyful feeling of spiritual growth" in the learner. He summarizes in particular:
“More important is the insight that the content of the education cannot be properly understood without the student himself following the“ path ”that leads to them, at least in a simplified form. Content and method are inextricably linked in a correlative manner. The content contains the path on which it became content - it cancels this path within itself; but the way, d. H. the direction in which the question is asked and the methodological steps necessarily always establish a certain perspective, determine in advance the way in which the content will light up at the end of the path. "
Klafki's review of Wagenschein's course was the subject of several scientific publications.
Classification in today's school context
The transition from Galileo's law of fall to the law of gravity is usually discussed in the so-called introductory phase (first half of 11th grade high school or level E). The gravitation near the earth's surface is the basis for practically all "earthly" falling processes; Using the law of inertia and the principle of independence , the free fall is extended to throws and the parabola is thus explained.
In today's school practice, physics experiences an increasing mathematization in the transition from lower secondary level to upper secondary level . In contrast, Wagenschein focuses more clearly on the historical change in the worldview of its time.
The interpretation of the sickle shape and the elementary determination of the size and distance of the sun and moon, to which Wagenschein dedicates the first half of his course, can usually not be dealt with in physics, but the second mentioned sometimes in mathematics lessons.
The lesson
Martin Wagenschein's course is the basis for a lesson in didactics of the art of teaching , which has so far been available in two variations. In addition, many parts have been treated by numerous teachers as an integral part of normal lessons and in projects.
Ahrens' lesson
In the years from 1997 onwards, the didactic teacher Daniel Ahrens developed the second part of Wagenschein's course, which is related to Newton, into an eight to ten hour-long teaching piece in which Newton appears as a character.
Ahrens didactic piece bears the unofficial title "As on earth, so also in heaven?" And stays close to the pull question "Why doesn't the moon fall?" In an overture, Newton introduces himself and reads from a historical script that he wrote in the Close to Aristotle. The question arises as to whether the moon is held in its orbit by the same forces that we know from earthly things. Different theories can be put forward, which usually leads to different preferences within the student body.
In the actual first act entitled “The Moon - A Thrown Body?” Newton presents his thought experiment from 1688. The principle of inertia and the superposition principle are also discussed again. The thesis is discussed from different perspectives.
The somewhat longer second act (“Is it really the gravitational pull?”) Now tries to critically and quantitatively check whether Newton's approach is tenable. It begins with a kind of interlude in which the elementary orbit speed of the moon is calculated. The search is now for a “fingerprint” of earthly gravity. A characteristic of the law of fall, known to the students, is that a falling body covers a fall distance of around five meters within one second. It is a little more difficult to calculate the distance the moon will fall in the direction of the earth during this time, since the pocket calculators, not yet in use at Wagenschein's time, sometimes "round off" to zero. If the invoice is sent, a value of only 1.3 mm can be determined.
The third and final act (“Relationships between Heaven and Earth”) concerns the genetic interpretation of this deviation. The introduction to the square traps with the distance from the Earth's center is managed via the decay of sound and light along a sphere, which eventually leads to the durchzudiskutierenden realization that earthly laws but would also be valid for the moon.
The poem Herbst by Rainer Maria Rilke is presented as the finale and conclusion and the students have the task of writing a letter to the author in which they explain to him that and why the poem can also be understood as astronomical . As a final reflection, this is intended to secure the knowledge gained.
Although Ahrens can not flow in the first part of Wagenschein course in his lesson, he had proposed Wagenschein afterlife of distance measurement in 2003 of the Moon by Lalande and Lacaille with a Lippstädter drilled classroom and in a competition organized by the Federal Ministry for Economic Cooperation and Development with the title "all for ONE WORLD - ONE WORLD for all" led to second place. Analogous to Lalande in Berlin at the time, his class had cooperated from Lippstadt with a school in Cape Town that had taken Lacailles’s place.
Eyers didactic draft
A somewhat more comprehensive draft for Wagenschein's course, which deals with almost the entire Wagenschein course, but has not yet been tested in its entirety in one piece, has existed since 2014 at the teaching arts didactic specialist Marc Eyer from the PH Bern , who developed it immediately after his second dissertation in Marburg . Eyer's draft can be divided into roughly three acts and should take at least twelve lessons, some of which are outside of the usual hours.
The overture begins in the evening sky with the contemplation of the crescent moon, which requires a freshly waxing moon. A Socratic conversation leads to the realization that the sun must be much further away than the moon.
The first act, which deals with most of the remainder of Wagenschein's celestial geometry, begins with the re-enactment of the measurements by Lalande and Lacaille from 1752. Eyer envisages a similar path to the one Ahrens took in 2003 on the occasion of the competition, and he suggests to compare own measurements in Bern with those of a partner class in Cape Town. Before that, however, Wagenschein's considerations about the relationship between the distance of the sun and that of the moon, as they had led Aristarchus to measure his crescent moon around 264 BC, are understood. After the distance to the moon has been determined, the calculation of the size of the moon, which is true to the original at Wagenschein, is carried out using a plate (the corresponding calculation for the size of the sun is saved for later). The parallax becomes the explicit theme.
The second act has to take place again in the evening sky. It involves observing the moon with a telescope and leads to understanding it as a “raging ball of rock”. After calculating its orbital speed, Newton's thesis that the moon obeys earthly laws is finally put into the space. Since students today usually “ think their “ universe ” “ much bigger ” from the outset , a look back at the time of Galileo is cast.
The third act begins with Newton's thought experiment and then leads in the verification and modification to the well-known formula.
In the finale, the pupils should first turn to the satellite himself in a "quiet meeting with the moon", if possible in the evening, and finally, as a reflection, send a letter to Newton with their findings and questions.
Comparison of the didactic concepts
The following table shows that Eyer tries to integrate almost the entire Wagenschein course, while Ahrens' didactic piece is clearly limited to the second half:
| Subject / question in Wagenschein's template | Action | findings | Ahrens | Eyer |
|---|---|---|---|---|
| View of setting sun with crescent moon (2) | Socratic conversation | a) Origin of the moon phases b) The moon is closer to us than the sun c) The sun is much larger than the moon |
overture | |
| How many times further away is the sun than the moon? (5.6 / 5.7) | Historical measurement of Aristarchus around 264 BC at a half moon | The sun is 400 times lower in space than the moon | ||
| How far is the moon? (5.8) | Historical measurement of Lalande and Lacaille from 1752 (triangulation) | The moon is 30 globes away | 1st act a | |
| How big are the sun and moon? (5.9 / 5.10) | Theorem of rays | a) The moon is four times smaller than the earth b) The sun is 400 times the size of the moon |
1st act b | |
| Migration of the moon through the zodiac band (5.12) | Wagenschein: Teaching requirement: "... careful evidence for the spherical shape and the axis rotation of the earth" | a) The moon moves close to the ecliptic through the zodiac b) The sun and also the planets do this, with slight deviations, also c) In particular, the orbits are approximately on one plane |
||
| How fast is the moon on its orbit around the earth? (5.13) | invoice | He storms through about 1 km per second! | 2nd act | 2nd act ("raging rock ball") |
| What brings the moon on its orbit? (5.14–5.16) | Newton's thought experiment from 1688 with sketch | a) The moon falls and yet does not get any closer to the earth b) A law encloses the well and the moon |
Overture / 1st act |
3rd act a |
| Does gravity even reach the moon? (5.17–5.20) | Does the moon's orbit meet the mark of gravity? (Invoice) |
a) The moon does not deviate by 5 m, but only by 1.3 mm from the straight path in one second. b) The force of gravity dilutes (decreasing quadratically) into space. |
a) 2nd act b) 3rd act |
3rd act b |
| <without equivalent in the vehicle license> | Spiritual follow-up of what has been learned | Ahrens: Letter to Rilke Eyer: Quiet discussion with the moon, reflection and letter to Newton |
final | final |
literature
The following list is arranged chronologically:
- Werner Heisenberg : Changes in the fundamentals of the natural sciences. S. Hirzel, Leipzig 1935; DNB 573732590
- Martin Wagenschein : The Tübingen Conversation in: Die Pädagogische Provinz 5 (1951) 12; Pp. 623-628; Online reprint (PDF; 90 kB)
- Martin Wagenschein: The "exemplary teaching" as a way to renew the higher school (with special attention to physics). Lecture at the Institute for Teacher Training in Hamburg on Nov. 26, 1952; extended version Hamburg 1954, DNB 455336245 ; in Wagenschein (1980): pp. 170-194
- Martin Wagenschein: From a physical point of view, nature. A handout on physical science for teachers of all types of schools. Diesterweg, Frankfurt / Berlin / Bonn 1953; DNB 455336288 , therein in particular
- The law of fall in the well jet (PDF; 660 kB)
- The moon and its movement (PDF; 760 kB)
- Martin Wagenschein: The earth under the stars. A path to the stars for each of us. Oldenbourg, Munich 1955, DNB 455336210 . Online reprint ; (PDF; 530 kB)
- Wolfgang Klafki : The pedagogical problem of the elementary and the theory of categorical education (= Göttingen studies on pedagogy . NF booklet 6). Beltz, Weinheim / Berlin 1957, DNB 480765197 . (Dissertation University of Göttingen, Philosophical Faculty)
- Wolfgang Klafki: Studies on educational theory and didactics . Beltz, Weinheim / Bergstrasse 1963; DNB 452 428 467 ; in this:
- Second study: categorical formation. For the educational theory interpretation of modern didactics. In: Zeitschrift für Pädagogik , 5th year 1959, pp. 386–412
- Martin Wagenschein: The Experience of the Globe. Klett, Stuttgart 1967, DNB 740557777 . Online reprint (PDF; 400 kB)
- Ueli Aeschlimann: With a car license to the art of teaching. Design, testing and interpretation of three teaching examples on physics, chemistry and astronomy using the genetic-dramaturgical method. Marburg 1999; DNB 969920059 ( download of the original dissertation ), therein:
- "Elementary celestial science" - a third lesson (pp. 121–193)
- Daniel Ahrens: "It is only half visible and yet it is round and beautiful" - investigation into the religious dimension of physics lessons using the example of elementary celestial science. Marburg 2005; DNB 978914600 ( download of the original dissertation ), therein (pp. 278–293):
- Lippstadt and Cape Town reach for the stars - determination of the size of the earth and the distance to the moon with simple means. Spectrum of Science, Heidelberg 2008 ( Download )
- Ulrike Harder: didactics of teaching art and Klafki's early educational didactics. Teaching trials in three didactic pieces: Goethe's "Italian Journey" - Athens in the era of Pericles - The Bassermanns. Citizenship in Germany through nine generations. Marburg 2012; DNB 1035627701 ( download of the original dissertation ), therein:
- Section 2.4. (Pp. 39–66) with strong reference to Klafki's review of Wagenschein's course
- Michael Jänichen: Dramaturgy in the teaching piece: celestial clock and terrestrial globe - Howard's clouds - earth exploration with Sven Hedin. A contribution to the theory, practice and poiesis of teaching arts didactics. Marburg 2010; DNB 1010690728 ( download of the original dissertation ), therein:
- Celestial clock and terrestrial globe (pp. 101–184)
- Marc Eyer: Lehrstück lesson in the horizon of cultural genesis. Didactic didactic composition and staging of Galileo's law of the fall - Pascal's barometer - Fermat's mirror optics. Marburg 2013; DNB 1049818873 ( download of the original dissertation , reprint: Springer, Wiesbaden 2015; ISBN 978-3-658-10997-4 ), therein:
- The law of fall according to Galileo (pp. 146–222)
- Marc Eyer: The moon and its movement. A lesson based on Martin Wagenschein. Lesson sketch, Marburg, May 2014
- Daniel Ahrens: As on earth, so also in heaven. Lehrstückbericht, Paderborn 2015 and Marburg 2017
- Benjamin Günther: Educational potential of subjects using the example of Martin Wagenschein's lesson design “The moon and its movement”. A theoretical investigation based on Wolfgang Klafki's categorical formation. Marburg 2015
Footnotes
- ↑ cf. Car license (1953)
- ↑ s. Klafki (1957)
- ↑ cf. Klafki (1959)
- ↑ s. Car license (1955)
- ↑ cf. Heisenberg (1935), p. 38
- ↑ Final remark in section 2
- ↑ Section 3
- ↑ Section 4
- ↑ Sections 5.1 to 5.10 take up this part.
- ↑ This realization can also come quickly to the layman when he considers that there are both total and annular solar eclipses ; so the moon appears sometimes a little larger and sometimes a little smaller than the moon.
- ↑ These considerations are briefly summarized in 5.1 to 5.4.
- ↑ s. 5.5 to 5.7
- ↑ cf. 5.8.
- ↑ cf. 5.9 and 5.10.
- ↑ cf. 5.11.
- ↑ cf. 5.12.
- ↑ cf. 5.13.
- ↑ cf. 5.14.
- ↑ cf. 5.15.
- ↑ cf. 5.16.
- ↑ cf. 5.17.
- ↑ cf. 5.18.
- ↑ cf. 5.19.
- ↑ cf. 5.20.
- ↑ cf. 5.21.
- ↑ cf. 5.22.
- ↑ cf. 5.23.
- ↑ This is the complete content of the final section 5.24.
- ↑ cf. Klafki (1959) in Klafki (1963), p. 43
- ↑ cf. Klafki (1959) in Klafki (1963), p. 40
- ↑ cf. Klafki (1959) in Klafki (1963), p. 41
- ↑ see e.g. Harder (2012) and Günther (2015)
- ↑ s. Ahrens (2015/2017)
- ↑ This assigns Wagenschein to his annus mirabilis 1665/66, which, however, is not tenable!
- ↑ cf. Ahrens (2006), pp. 278 ff, and Ahrens (2008).
- ↑ s. Eyer (2014)
- ↑ s. Eyer (5'2014)
- ↑ The table is based on a list by Ahrens from June 2014, but has been supplemented a little.