Post AaUSbWGbGFFED92KFk by toybox@framapiaf.org
 (DIR) More posts by toybox@framapiaf.org
 (DIR) Post #AaUCrAb7zjQCNB4y1Y by futurebird@sauropods.win
       2023-10-05T17:37:23Z
       
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       Thousands of students hit a wall at algebra and calculus because of this aspect of notation. The tendency of more basic courses and examples to omit ratio representation doesn’t help. I have a student who is very process focused (the procedures are safe! reliable) but I’m worried she thinks each of these is a totally different function. Does this mean that ratios never clicked for her? Or is this just about “experience” and with time you are confident that these are all the same beast?
       
 (DIR) Post #AaUCrBOP2Wpwq08JpQ by toybox@framapiaf.org
       2023-10-05T19:14:34Z
       
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       @futurebird Even though they're all equal, they all say something different to me (like (2/3)x means I have x things and want two thirds of it, and (2x)/3 means I somehow ended up with twice of something and now have to divide it in three parts).
       
 (DIR) Post #AaUCrCGHoBwFX7LLoe by futurebird@sauropods.win
       2023-10-05T17:38:31Z
       
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       Most problem sets avoid this stuff and if a student isn’t playing with notation on their own I can understand the confusion.
       
 (DIR) Post #AaUCrCLxT6TXohzsem by toybox@framapiaf.org
       2023-10-05T19:18:06Z
       
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       @futurebird And really the same goes for multiplication: like 7x55 is, I have little bags of 55 whatevers and take 7 bags of it, while 55x7 would mean I have boxes of 7 whatevers and I get 55 boxes.Sometimes I think we are too used to things like AxB = BxA, when it should just really surprise us. I mean, why do 7 bags of 55 contain the same amount than 55 boxes of 7, really.
       
 (DIR) Post #AaUCrCyFAl6HjRuSKe by hayley@social.applied-langua.ge
       2023-10-06T07:23:45.201872Z
       
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       @lispi314 @toybox @futurebird I recall getting X bags of Y whatevers the wrong way around when I was ~8 in primary school, and the teacher would not let me off because "it was the same number".
       
 (DIR) Post #AaUQM1pdw1BvZDugam by tusooa@kazv.moe
       2023-10-06T09:54:55.673687Z
       
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       @futurebird 2x(1/3) is ambiguous. if x can be a function it can have different meanings.
       
 (DIR) Post #AaUSbWGbGFFED92KFk by toybox@framapiaf.org
       2023-10-06T10:19:51Z
       
       1 likes, 0 repeats
       
       @hayley @lispi314 @futurebird Oh, that's harsh. You can really interpret 4x5 as 4 bags of 5 things, or as bags of 4 things which you have 5 of, and it's essentially a matter of taste.I remember in one of the unis I went to, algebraist were divided in two factions according to similar views.