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^"permissions":^"read":ӶӺ,"update":ӶӺ,"delete":ӶӺ,"admin":ӶӺ°,"user":^"id":6,"name":"Sarah Oberbichler"°,"id":"V9qo4j2dns","ranges":Ӷ^"start":"/divӶ3Ӻ/divӶ4Ӻ/divӶ1Ӻ/pӶ47Ӻ","startOffset":0,"end":"/divӶ3Ӻ/divӶ4Ӻ/divӶ1Ӻ/pӶ50Ӻ","endOffset":1559°Ӻ,"quote":"This brings me to a point which, I believe, is indispensable for didactics. There is no infallible method of teaching conceptual thinking. But one of the most successful consists in presenting students with situations in which their habitual thinking fails. I shall lay out an example of this method that was developed by Leonard and Gerace at our institute at the University of Massachusetts.\nHere you have a schematic representation of an apparatus that reminds me of a game that we passionately played as children, if there was a big heap of sand or at the beach. We made a kind of bobsleigh track, and let our large glass marbles roll down to see which was the fastest.\n\n\n\nWhat you see here, are two tracks on which steel balls can roll with almost no frictional loss of energy. The two tracks are not the same, but start and finish are on the same height for both. The question is, which of the two balls will reach the finish first, if they are started at the same time?\nMany of the beginning physics students to whom the question is put, say that number 1 will arrive first, because number 2 has a longer path.\nOthers predict that the balls will arrive simultaneously, because, although number 2 gains a lead on the downhill slope, it will lose it when it has to roll uphill.\nVery rarely one answers that number 2 will win the race.\nHence there is considerable surprise when the balls are actually let roll, and number 2 arrives first every time. Some of the students laugh and say that we have somehow managed to build a trick into the display.\nWe assure them that there is no trick, and ask them to describe, as accurately as they can, what happens on each of the sections of the track.\nAt first it is often not easy to get them to talk. But when we assure them that this is not a test and that we merely want them to share with the others what they are thinking, one or two begin, and then others join in. It usually does not take long for them to agree on the following descriptions:\nAt point A, both balls arrive at the same moment and with the same speed.\nThe slope from A to B accelerates number 2 and it therefore reaches point B before number 1.\n– “Number 2 has a lead?” we ask.\nYes. At point B, number 2 has a lead – but then it has to roll uphill and it loses its lead.\n– We ask: “And when number 2 reaches point C, does it roll faster or slower than number 1?\nUsually this triggers a longer discussion, but eventually the students agree that the negative acceleration on the uphill section equals the positive acceleration on the downhill and therefore the two balls should have the same speed at point C.\nThis is the moment when some catch a glimpse of the insight that number 2 rolls faster than number 1 over the entire stretch from A to C. The lead it gains does more than cover the longer path, and therefore it arrives first at the finish.\nOf course, not all the students are immediately convinced. But those who have seen the solution are usually indefatigable in explaining it to others. In the end, most of them understand how, as physicists, they have to conceptualize the situation.","highlights":Ӷ^"jQuery3210115457946860578312":^°°,^"jQuery3210115457946860578312":^°°,^"jQuery3210115457946860578312":^°°,^"jQuery3210115457946860578312":^°°,^"jQuery3210115457946860578312":^°°,^"jQuery3210115457946860578312":^°°,^"jQuery3210115457946860578312":^°°Ӻ,"text":"","order":"mw-content-text","category":"Argumentation2","data_creacio":1594906019497°
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