michael_nielsen on Twitter: "Re the initial tweet: that's amazing. Cf what I wrote in the essay Bushra cited later. I think @CTZN5 is right: what's meant by "correct" seems really subtle. Understanding the equals sign (or any other deep piece of mathematics) is open-ended.… https://t.co/Nt7HPbAnPJ"

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Bushra Farooqui‏ @startuployalist Jun 19

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This entire study is fascinating: Those who “exhibit the correct understanding of the equal sign show the greatest achievement in mathematics and persist in fields that require mathematics proficiency like engineering”pic.twitter.com/R38oj2EQGB

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Bushra Farooqui‏ @startuployalist Jun 19

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The idea of symbols conveying relative meaning is complex. This understanding becomes foundational, supporting greater comprehension through advanced math:pic.twitter.com/pNW4IW4wSf

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Bushra Farooqui‏ @startuployalist Jun 19

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The press-button-and-calculate or “running equal sign” tends to miss the relational understandingpic.twitter.com/5EmSc5J2Z7

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Bushra Farooqui‏ @startuployalist Jun 19

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Can read the rest here: http://educationresearchreport.blogspot.com/2010/08/students-understanding-of-equal-sign.html?m=1 … And relatedly: - https://www.intmath.com/blog/mathematics/the-equal-sign-more-trouble-than-its-worth-4986 … - http://cognitivemedium.com/srs-mathematics (ht: @michael_nielsen)

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JJ 「cιtιƶεɳƒιvε」 ‏ @CTZN5 Jun 19

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Replying to @startuployalist @michael_nielsen

Interesting as a predictor. Further comments: 1. Be sure to differentiate between the "running equal sign" as described, which places unequal expressions across the equality/equals sign, and perfectly legitimate uses during simplifications and identity transformations

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JJ 「cιtιƶεɳƒιvε」 ‏ @CTZN5 Jun 19

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Replying to @CTZN5 @startuployalist @michael_nielsen

For example, when preparing a child for encounters with PEMDAS—which by its own universe rules should be probably taught as PE(M/D)(A/S)—and order of operations, it is useful to begin with an exercise of absurd expansion:

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JJ 「cιtιƶεɳƒιvε」 ‏ @CTZN5 Jun 19

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Replying to @CTZN5 @startuployalist @michael_nielsen

We'll do things like – Make explicit the implicit parentheses – Re-express subtraction as addition by a negative – Express negative operands each instead as a positive operand multiplied by the negative identity – Declutter/unfuck divisors and exponentiation

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michael_nielsen‏ @michael_nielsen Jun 19

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Replying to @CTZN5 @startuployalist

I must have missed the day in school when they taught us to declutter/unfuck divisors and exponentiation. A rare case of a lesson I am sorry to have missed. (Joking aside: interesting how tacit so much of this is.)

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michael_nielsen‏ @michael_nielsen Jun 19

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Replying to @michael_nielsen @CTZN5 @startuployalist

Re the initial tweet: that's amazing. Cf what I wrote in the essay Bushra cited later. I think @CTZN5 is right: what's meant by "correct" seems really subtle. Understanding the equals sign (or any other deep piece of mathematics) is open-ended.pic.twitter.com/erjiQ63Vga

4:58 PM - 19 Jun 2019

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1. joe ‏ @latone Jun 19
  
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  = is Buddhist: highly tolerant, requires a great deal of faith, and the legend of its creator is illuminating. E.g., in Euler’s, two paths with the same destination:pic.twitter.com/z4h2vJ1q1a
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1. Austen Lamacraft‏ @AustenLamacraft Jun 20
  
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  I wonder (as one commenter speculated about the blog post) whether calculators are to blame for this one. I do remember the magical realisation that you could do whatever you wanted to an equation as long as you did it to both sides.
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