iiinova — where your digital self keeps evolving

💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @smartmanapps.dotnet.social.ap.brid.gy · 31/08/2026

5/7 "both way to write things make sense" - Nope, writing 1/ab for (1/a)xb makes no sense at all, as it contradicts literally every textbook ever "There is only one solution" - READ MATHS TEXTBOOKS 🙄 "avoids the brackets" - not only does 1/ab avoid brackets […] [Original post on dotnet.social]

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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @smartmanapps.dotnet.social.ap.brid.gy · 24/08/2026

5/7 "This is natural if one looks as division and multiplication as operations on the same level" - but it's UN-natural to consider a Term as "Multiplication" - it's a Product, the RESULT of a Multiplication "the division is on the left" of the term 3x, and […] [Original post on dotnet.social]

screenshot of website for kids spelling out that multiplicand x multiplier = product

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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @smartmanapps.dotnet.social.ap.brid.gy · 06/08/2026

P.S. I forgot to say this when I wrote this thread (had intended to), but for those where I posted the context-less textbook screenshot of 30÷10x3 - so as to try and not influence votes in the poll - here it is now with the full context restored (which was […] [Original post on dotnet.social]

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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @smartmanapps.dotnet.social.ap.brid.gy · 03/08/2026

4/6 The reason 18÷(3x2) is unambiguously wrong is the rule of Left Associativity. You can see in the textbook screenshot that for doing addition before subtraction, we add up all of the positive numbers, and then subtract the total of all the negative numbers […] [Original post on dotnet.social]

Textbook screenshot saying we take the total of the positive numbers and subtract the total of the negative numbers

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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @smartmanapps.dotnet.social.ap.brid.gy · 27/07/2026

1/6 #MathsMonday This week I'm kicking off a new #HallOfShame series, about spreaders of #disinformation #misinformation about #Mathematics, or as I call them, the #disinformati. Some have #Maths qualifications, some only have Physics(!) qualifications, and […] [Original post on dotnet.social]

screenshot from Oliver's PDF where he shows an e-mail to him from someone advising him that a user of Youtube called him (Oliver) an idiot, because of his blog post

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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @smartmanapps.dotnet.social.ap.brid.gy · 23/07/2026

Which has then reminded me of a time I took a screenshot of a big time ratio over at the old place...

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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @smartmanapps.dotnet.social.ap.brid.gy · 06/07/2026

1/10 #MathsMonday This article was referred to me - puzzlewocky.com/brain-teasers/proba… - and it's a classic case of #Mathematics #disinformation being spread by someone who […] [Original post on dotnet.social]

Picture of a card shuffling machine with a deck of cards loaded face up ready to go

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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @smartmanapps.dotnet.social.ap.brid.gy · 15/06/2026

4/4 I've sometimes had those types say to me "where can I find these rules listed in a Maths textbook?". You can't (which I'm sure they know). Each rule is in a relevant part of the text. e.g. you will find order of operations rules in a chapter about... order […] [Original post on dotnet.social]

A graphic listing out Curwen's rules of teaching from 1886

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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @smartmanapps.dotnet.social.ap.brid.gy · 15/06/2026

1/4 #MathsMonday #Mathematics #Math This week a note about the rules of #Maths, but first, the picture... I saw Mules get mentioned this week, and had a funny thought, "Mules works as an abbreviation of Mathematical Rules", which then lends itself to saying […] [Original post on dotnet.social]

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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @smartmanapps.dotnet.social.ap.brid.gy · 12/06/2026

@chemoelectric "It is a definition" - no, it's a rule, found in Maths textbooks, taught in school. The rules exist to prevent arriving at wrong answers "When you use it in a proof, you are applying a" rule "One could as easily have defined it right […] [Original post on dotnet.social]

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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @smartmanapps.dotnet.social.ap.brid.gy · 01/06/2026

2/3 In fact the first time students see this is in Primary School, when they can do it for themselves with Cuisenaire Rods. In the picture we can see an orange rod of length 10, and next to it a blue rod of length 9, and a white cube for 1, and we can see that […] [Original post on dotnet.social]

Picture of Cuisenaire Rods, description in post text

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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @smartmanapps.dotnet.social.ap.brid.gy · 01/06/2026

1/3 #MathsMonday #Math I've seen 2 people in #Mathematics claim recently that we can't prove that a+b=b+a - the Commutative Property - and that we just accept it as true. Nope, not only is it literally proven, but we show students the proof when we teach this […] [Original post on dotnet.social]

Picture depicting the Commutative Property for Addition and Multiplication

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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @smartmanapps.dotnet.social.ap.brid.gy · 26/05/2026

[Long thread/4] @alberto_cottica "Is it some form of content warning" - yes "the logic" - there's a setting where you can not show posts with content warnings, therefore his followers will only see the condensed version of the thread unless they expand "Are […] [Original post on dotnet.social]

Bernie Sanders meme, saying "I am once again asking that you not put the same hashtags in every post in your long thread"

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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @smartmanapps.dotnet.social.ap.brid.gy · 18/05/2026

5/5 ...and as is written by students for several years before they start using brackets. And when people say "the order of operations rules only exist so we can write fewer brackets", no they don't, given they were around for several centuries before we […] [Original post on dotnet.social]

Screenshot of Cajori saying "In those days when machine processes in printing were not in vogue, and when typesetting was done by hand, it was less essential than it is now that symbols should, in orderly fashion, follow each other in a line"

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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @smartmanapps.dotnet.social.ap.brid.gy · 18/05/2026

2/5 Scrolling further through Cajori's book you will find that the modern symbols for multiply, divide, and exponents all came along in the 17th Century, as did the modern form of Algebra. The order of operations rules have also been around for that long. In […] [Original post on dotnet.social]

Screenshot of Cajori saying "The constant stream of articles from Euler that appeared during the 18th Century contributed vastly toward accustoming mathematicians to their use"

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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @smartmanapps.dotnet.social.ap.brid.gy · 18/05/2026

1/5 #MathsMonday This week I will debunk several false claims made about brackets in #Mathematics on socials - there are several! Actually it's easy to just check for yourself, at […] [Original post on dotnet.social]

Screenshot from Cajori showing early Egyptian arithmetic, and that + and - came into use in Germany at the end of the 15th Century

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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @smartmanapps.dotnet.social.ap.brid.gy · 15/05/2026

@erikcats "get another hobby" - in case you missed it, it's my profession. I also teach Computer Science. And in case you missed it, Predictive Text is implemented on usernames as well (which you're way down the list in my case, because Predictive Text) 🙄 Next […] [Original post on dotnet.social]

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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @smartmanapps.dotnet.social.ap.brid.gy · 15/05/2026

@erikcats "there's no algorithm " - apps can't work without algorithms, it's just a matter of what the algorithms do. ActivityPub is implemented with algorithms. The Home feed has an algorithm. It's all algorithms "so how would this even work?" - the same way […] [Original post on dotnet.social]

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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @smartmanapps.dotnet.social.ap.brid.gy · 15/05/2026

@erikcats "Is this #Mastodon wide?" - I don't think so no. I think the defaults start out as lower-case, but I've consistently used Pascal-case, and now it starts to anticipate that's what I want (but I did have to type words out in full for a while to get it […] [Original post on dotnet.social]

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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @smartmanapps.dotnet.social.ap.brid.gy · 15/05/2026

@phocks "there’s no beta-male woke nonsense about wearing a helmet to ride a motorbike" - OMG. Spot the 2 problems in this still! I'll reply with spoiler alert for those who don't see them...

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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @smartmanapps.dotnet.social.ap.brid.gy · 13/05/2026

@phocks Sadly, mornings are no longer good. Best we can hope for now is a good afternoon

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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @smartmanapps.dotnet.social.ap.brid.gy · 27/04/2026

2/6 I bring this up as I've several times seen people think/claim these are actual rules of Maths to be obeyed, and they're not! Sometimes it's just misguided ignorance about scaffolding in textbooks, but other times it is a deliberate misrepresentation by […] [Original post on dotnet.social]

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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @smartmanapps.dotnet.social.ap.brid.gy · 27/04/2026

1/6 #MathsMonday This week #scaffolding, as used in #Mathematics (and other) #textbooks, as I'll be referring to this in two upcoming #Maths threads. The name is taken from the scaffolding used when buildings are being erected, and removed when construction is […] [Original post on dotnet.social]

Picture of a half-built house surrounded by scaffolding and a builder standing on the top

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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @smartmanapps.dotnet.social.ap.brid.gy · 22/04/2026

@mark "We invent these tools to mediate that gap" - Maths was discovered, not invented "To be fair, this is way past sciences and into philosophy." - nope. It's still science. "I think you would argue that absent all human minds math would still exist" - took […] [Original post on dotnet.social]

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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @smartmanapps.dotnet.social.ap.brid.gy · 22/04/2026

@mark "In what form?" - in every form "Atoms certainly don't care how many of themselves there are" - and yet sub-atomic particles were discovered from doing the Maths "Nor do they describe the rules by which they interact other than existing and doing it" - […] [Original post on dotnet.social]

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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @smartmanapps.dotnet.social.ap.brid.gy · 21/04/2026

@mark "The crushed plants have chemical reactions but don't "care."" - and yet they are crushed nonetheless "a human description of the phenomena" - which happens REGARDLESS of the human description of it 🙄 "stuff just happens" - yep, MATHS just happens 🙄 […] [Original post on dotnet.social]

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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @smartmanapps.dotnet.social.ap.brid.gy · 21/04/2026

@mark the damage magically appears, now that someone is there to observe it. Yeah sure dude 🙄 "I have no disagreement that things exist independently of the words that we use to name them" - such as Maths 🙄 "My only claim is that math is the words not the […] [Original post on dotnet.social]

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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @smartmanapps.dotnet.social.ap.brid.gy · 19/04/2026

@upworthy.com Gen X discovering that one of their words was apparently out of fashion in the 90's, but is back in fashion now anyway, so all good! History never repea... oh wait 😂

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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @smartmanapps.dotnet.social.ap.brid.gy · 13/04/2026

1/9 #MathsMonday #Mathematics This rubbish article www.scientificamerican.com/article/… popped up in my feed a few times, and I've already debunked the various points, but will cover it with specific […] [Original post on dotnet.social]

Graph of the hyperbola 1/x, showing that it never reaches 0

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💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱 @smartmanapps.dotnet.social.ap.brid.gy · 08/04/2026

If you thought the kids would be getting tired of #67 by now, think again

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